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NAG[g05lbc] NAG[nag_rngs_students_t] - Generates a vector of random numbers from a Student's  -distribution, seeds and generator number passed explicitly
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Calling Sequence
g05lbc(df, n, x, igen, iseed, 'fail'=fail)
nag_rngs_students_t(. . .)
Parameters
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df - integer;
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On entry:  , the number of degrees of freedom of the distribution.
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Constraint:  . .
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n - integer;
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On entry:  , the number of pseudo-random numbers to be generated.
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Constraint:  . .
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x - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array x must be at least  .
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On exit: the  pseudo-random numbers from the specified Student's  -distribution.
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iseed - Vector(1.. , datatype=integer[kernelopts('wordsize')/8]);
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On entry: contains values which define the current state of the selected generator.
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On exit: contains updated values defining the new state of the selected generator.
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_rngs_students_t (g05lbc) generates a vector of pseudo-random numbers taken from a Student's  -distribution with  degrees of freedom.
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Description
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The distribution has PDF (probability density function)
nag_rngs_students_t (g05lbc) calculates the values
![y[i]*sqrt(nu/z[i])*i = 1, () .. (), n](/support/helpjp/helpview.aspx?si=9898/file08494/math123.png)
where the ![y[i]](/support/helpjp/helpview.aspx?si=9898/file08494/math126.png) are generated by g05lac (nag_rngs_normal) from a Normal distribution with mean 0 and variance  , and the ![z[i]](/support/helpjp/helpview.aspx?si=9898/file08494/math133.png) are generated by g05lfc (nag_rngs_gamma) from a gamma distribution with arguments  and 2 (i.e., from a  -distribution with  degrees of freedom).
One of the initialization functions g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_students_t (g05lbc).
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Error Indicators and Warnings
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"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
On entry,  . Constraint:  .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
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Further Comments
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The time taken by nag_rngs_students_t (g05lbc) increases with  .
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Examples
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>
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df := 5:
n := 5:
igen := 1:
x := Vector(5, datatype=float[8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05lbc(df, n, x, igen, iseed):
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